Hamiltonianminimal Lagrangian submanifolds in toric varieties
Abstract
Hamiltonian minimality (Hminimality) for Lagrangian submanifolds is a symplectic analogue of Riemannian minimality. A Lagrangian submanifold is called Hminimal if the variations of its volume along all Hamiltonian vector fields are zero. This notion was introduced in the work of Y.G. Oh in connection with the celebrated Arnold conjecture on the number of fixed points of a Hamiltonian symplectomorphism. In the previous works the authors defined and studied a family of Hminimal Lagrangian submanifolds in complex space arising from intersections of Hermitian quadrics. Here we extend this construction to define Hminimal submanifolds in toric varieties.
 Publication:

Russian Mathematical Surveys
 Pub Date:
 April 2013
 DOI:
 10.1070/RM2013v068n02ABEH004835
 arXiv:
 arXiv:1301.2679
 Bibcode:
 2013RuMaS..68..392M
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Geometric Topology
 EPrint:
 2 pages, minor changes in version 2